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Problem 48 Medium Difficulty

Where does the line through $ (-3, 1, 0) $ and $ (-1, 5, 6) $ intersect the plane $ 2x + y - z = -2 $?

Answer

$(0,7,9)$

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Video Transcript

Hello. So the question is taken from vectors in geometry of the space And we have to find where does the line to -310 N -156 intersects the plane. So that it Equation of lying there passing to the .31 jail. Mhm And minus one 56. So it is simple to evaluate it. That is X. Subtracting this minus three. From here We get Express three and keeping like this by -1. Write it like this and set zero divided by -1 plus two. This is the normal way to where the equation of line which passes to these 2.5 -1 divided by 6 0. So that will be X-plus three x 2 which is equal to buy minus one by four is equal to that by six. Okay so let me get this equal to some phones 20 so actually be equal to 20 minus three. And why is equal to 40 plus one. And that is a call to 66 cents 30. So let me substitute this value of X. Y. Zed in the plane. In order to evaluate at which point that their line intersect with the plane. So that plane will be to wait plus y minus zed. It is like that T. Is a kind of point. He's basically consists all those points from at least one of the points which intersect. We have to find at least one of the points. That is from the value of T. At which the line intersect with the plane and that is they minus eight is sorry is equal to minors of substituting the value of X. Y. Z. We get Going to do T -3 Plus 40 plus one -60 is equal to minus of the so we get 40 -6 Plus 40 plus one -60 is equal to minus of food. So they will use us. 8 -6 is duty -6. Plus one is -5 is equal to -2. So that reduces to T. is equal to three. So from here T is equal to 1.5 substituting the value of T. Here we get the point from which the line passes is X. is equal to 20-2, 202.1.5 -30. And why is it? Well too 40 plus Form four into Thi is 1.5 so six Plus one so that will be sent and that is equal to 66 into 1.5 with equal to nine. So the point to which that plane align intersected 079 so which which is required solution of decoration. Hope this clears it out and